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Understanding Area Lesson 11.1

Understanding Area Lesson 11.1. Units of measure 1. Linear units: perimeter, circumference 2. Square units: area 3. Cubic units: volume. Definition: The area of a closed region is the number of square units of space within the boundary of the region. Area of a rectangle:

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Understanding Area Lesson 11.1

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  1. Understanding AreaLesson 11.1

  2. Units of measure 1. Linear units: perimeter, circumference 2. Square units: area 3. Cubic units: volume Definition: The area of a closed region is the number of square units of space within the boundary of the region.

  3. Area of a rectangle: Arect = bh where b is the length of the base and h is the length of the height. Theorem 99: the area of a square is equal to the square of a side. Asq = s2 where s is the length of a side.

  4. Postulate: every closed region has an area. If two closed figures are congruent, then their areas are equal. If ABCDEF is congruent to LMNOPQ, then the area of region 1 is equal to the area of region 2. L M B A F 1 Q 2 N C D P O E

  5. Postulate: If two closed regions intersect only along a common boundary, then the area of their union is equal to the sum of their individual areas. + =

  6. To solve these problems: Write the correct formula Plug in the correct numbers Compute and give answer with correct units. (minimum 3 lines!) For irregular shapes, divide it into individual shapes, solve each shape and then add together.

  7. 13m 3m 3m 8m 3m 3m Example: Find the area of the shape below. Method 1 Divide the shape into 3 rectangles. Find the area of each rectangle. Add the areas together.

  8. 13m 3m 3m 8m 3m 3m A = bh + bh + bh = 3(8) + 14(13) + 3(8) = 24 + 182 + 24 = 230m2

  9. 13m 3m 3m 8m 3m 3m Method 2 Calculate the base and height of the original rectangle, find total area. Calculate the area of the 4 corners. Subtract the 4 corners from the total area.

  10. 13m 3m 3m 8m 3m 3m A = bh-4s2 = 19(14) - 4(3)2 = 266 - 36 = 230m2

  11. 40ft Find the area of the walkway around the pool. 30ft 35ft 38ft A = bh – bh A = 40(35) – 38(30) A = 1400 – 1140 A = 260 ft2

  12. Time to Paint the Classroom… This classroom could use a fresh coat of paint. With your team, determine how many square feet will need to be painted. Keep your calculations secret until we reveal them to the class.

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